ASTRA Transport Code Research Articles

Turbulent-convective block for the ASTRA transport code

A physical model for the enhanced transport code is presented, which explicitly takes into account the contribution of turbulent convection to the processes of particle and heat transport in the hot core of the tokamak plasma. The model is based on the specially developed CONTRA-A turbulent block, while an adapted version of the existing ASTRA transport code is used as a transport envelope. The CONTRA-A turbulent block, based on the adiabatically reduced quasi-2D magnetohydrodynamic equations, calculates the generation and self-consistent evolution of low-frequency turbulence, including the spatiotemporal structure of turbulent fluctuations of the plasma velocity, density, and temperatures of electrons and ions. Using the obtained data on fluctuations, the CONTRA-A block calculates the turbulent-convective particle and heat fluxes and transfers them to the modified ASTRA code, which computes the evolution of quasi-equilibrium plasma parameters. To illustrate the capabilities of the enhanced transport model, the results of simulations of turbulent plasma evolution in two discharge scenarios with nonstationary auxiliary plasma heating in the T-10 and T-15MD tokamaks are presented.

Numerical and semi-analytical treatments of neutral beam current drive in DEMO-FNS

Neutral Beam Current Drive (NBCD) is considered as a highly attractive mechanism for a steady state regime in such contemporary projects as a tokamak based Fusion Neutron Source (FNS) or a DEMO type thermonuclear reactor. In this report numerical calculations of NBCD with a Monte Carlo code NUBEAM are complemented by a semi-analytical treatment of fast ion velocity distribution function. Spectral distributions of fast ions injected with neutral beams to FNS plasma are obtained for DEMO-FNS and a Spherical Tokamak Neutron Source FNS-ST. A detailed comparison of NUBEAM and semi-analytical approaches is presented on the basis of ASTRA transport code provided equilibrium data for different plasma regimes. The applicability of the semi-analytical approach is discussed.

A 0D stationary model for the evaluation of the degree of detachment on the divertor plates

A 0D analytical stationary model to estimate the degree of detachment on the divertor plates is derived, starting from previous works of Igitkhanov (Igitkhanov et al 1994 21st EPS (Montpellier) ECA v.18B, 1995 22th EPS (Bournemouth) ECA v.19C, Igitkhanov 2014 KIT Sci. Rep. 7661). It accounts for heat convection, conduction, impurity radiation and contains a simplified balance for the neutrals. The upstream particle flux (or, alternatively, the density upstream nup), the heat flux in the scrape-off layer (SOL) qup and the impurity concentrations are required as input, whereas the temperatures at the plate and at the separatrix are not fixed a priori. The routine has been mainly developed for system codes, or more in general for scopy studies in the framework of the preliminary design phase for the reactor DEMO, its simplicity being therefore justified by the purpose of keeping the calculation times as low as possible. A calibration against a more detailed 1D routine (Kallenbach et al 2016 Plasma Phys. Control. Fusion 58 045013) has been performed, finding a reasonable agreement. Furthermore, a coupling of the model with the 1.5D transport code ASTRA (Pereverzev 1991 IPP Report 5/42, Fable et al 2013 Plasma Phys. Control. Fusion 55 124028) to illustrate its possible usage is also presented.

Pioneering experiments on atomic-beam-assisted generation of drag currents in the Globus-M spherical tokamak

Research data for drag currents in the Globus-M spherical tokamak are presented. The currents are generated by injecting atomic beams of hydrogen and deuterium. Experiments were carried out in the hydrogen and deuterium plasma of the tokamak. It has a divertor configuration with a lower X-point, a displacement along the larger radius from–1.0 to–2.5 cm, and a toroidal field of 0.4 T at a plasma current of 0.17–0.23 MA. The beam is injected into the tokamak in the equatorial plane tangentially to the magnetic axis of the plasma filament with an impact diameter of 32 cm. To provide a 28-keV 0.5-MW atomic beam with geometrical sizes of 4 × 20 cm (at a power level of 1/e), an IPM-2 ion source is used. The generation of noninductive currents is detected from a rise in the loop current and a simultaneous dip of the loop voltage. The injection of the hydrogen and deuterium atomic beams into the deuterium plasma results in a noticeable and reproducible dip of the loop voltage (up to 0.5 V). Using the ASTRA transport code, a model is constructed that allows rapid calculation of noninductive currents. Calculations performed for a specific discharge confirm that the model adequately describes the effect of drag current generation.

Integrated modelling of DEMO-FNS current ramp-up scenario and steady-state regime

An approach to the integrated modelling of plasma regimes in the projected neutron source DEMO-FNS based on different codes is developed. The consistency check of the steady-state regime is carried out, namely, the possibility of the plasma current ramp-up, acceptance of growth rates of MHD modes in the steady-state regime, heat loads to the wall and divertor plates and neutron yield value. The following codes are employed for the integrated modelling. ASTRA transport code for calculation of plasma parameters in the steady-state regime, NUBEAM Monte Carlo code for NBI incorporated into the ASTRA code, DINA free boundary equilibrium and evolution code, SPIDER free boundary equilibrium and equilibrium reconstruction code, KINX ideal MHD stability code, TOKSTAB rigid shift vertical stability code, edge and divertor plasma B2SOLPS5.2 code and Semi-analytic Hybrid Model (SHM) code for self-consistent description of the core, edge and divertor plasmas based on the experimental scaling laws. The consistent steady-state regime for the DEMO-FNS plasma and the plasma current ramp-up scenario are developed using the integrated modelling approach. Passive copper coils are suggested to reduce the plasma vertical instability growth rate to below ∼30 s−1.The outer divertor operation in the ‘high-recycling’ regime is numerically demonstrated with a maximal heat flux density of 7–9 MW m−2 that is technically acceptable.

Integrated modelling of the Globus-M tokamak plasma and a comparison with SOL width scaling

Recently a scheme for the coupling of the one-dimensional core transport code ASTRA and the two-dimensional edge transport code B2SOLPS was developed, thus providing the integrated modelling of tokamak discharge. Here, this scheme is improved by taking impurities into account and by considering a real flux surface shape using the equilibrium code SPIDER. This integrated modelling is applied to discharges of the spherical tokamak Globus-M to study the dependence of the scrape-off layer (SOL) width and divertor heat loads on the discharge power and the plasma current. Since these values, together with the magnetic field, are relatively small in Globus-M, this study can test the existing scaling against data in a wider range of tokamak operational parameters. The modelling results agree reasonably with Thomson scattering and Langmuir probe measurements and allow, in principle, the determination of the physical mechanisms responsible for the SOL structure formation. It is found that the SOL width is approximately inversely proportional to the plasma current, in agreement with existing experimental scaling, while its dependence on discharge power is found to be quite weak.

Novel free-boundary equilibrium and transport solver with theory-based models and its validation against ASDEX Upgrade current ramp scenarios

Tokamak scenario development requires an understanding of the properties that determine the kinetic profiles in non-steady plasma phases and of the self-consistent evolution of the magnetic equilibrium. Current ramps are of particular interest since many transport-relevant parameters explore a large range of values and their impact on transport mechanisms has to be assessed. To this purpose, a novel full-discharge modelling tool has been developed, which couples the transport code ASTRA (Pereverzev et al 1991 IPP Report 5/42) and the free boundary equilibrium code SPIDER (Ivanov et al 2005 32nd EPS Conf. on Plasma Physics vol 29C (ECA) P-5.063 and http://epsppd.epfl.ch/Tarragona/pdf/P5_063.pdf), utilizing a specifically designed coupling scheme. The current ramp-up phase can be accurately and reliably simulated using this scheme, where a plasma shape, position and current controller is applied, which mimics the one of ASDEX Upgrade. Transport of energy is provided by theory-based models (e.g. TGLF (Staebler et al 2007 Phys. Plasmas 14 055909)). A recipe based on edge-relevant parameters (Scott 2000 Phys. Plasmas 7 1845) is proposed to resolve the low current phase of the current ramps, where the impact of the safety factor on micro-instabilities could make quasi-linear approaches questionable in the plasma outer region. Current ramp scenarios, selected from ASDEX Upgrade discharges, are then simulated to validate both the coupling with the free-boundary evolution and the prediction of profiles. Analysis of the underlying transport mechanisms is presented, to clarify the possible physics origin of the observed L-mode empirical energy confinement scaling. The role of toroidal micro-instabilities (ITG, TEM) and of non-linear effects is discussed.

Particle transport analysis of the density build-up after the L–H transition in ASDEX Upgrade

Predictive-iterative modelling has been performed to investigate the role of convective and diffusive particle transport in the edge during the density build-up after the L–H transition. For the time-dependent modelling, the 1.5D radial transport code ASTRA has been used. The convective velocity, diffusion coefficient and the particle source profiles have been parameterized. Their parameters were varied until the best match of the modelling to the density measurements was found. The extensive parameter scans show that the density build-up can be reproduced by assuming only a diffusive edge transport barrier (ETB) with reduced diffusion coefficient at the edge with respect to the core values. Moreover, the replacement of the diffusive ETB by a strong inwards directed convective velocity at the edge (edge pinch) did not succeed in describing the data. This indicates that a diffusive ETB is required to explain the density build-up. However, the addition of an edge pinch to the diffusive ETB barrier slightly enhances the agreement between modelling and experiment. The best agreement was found with an edge diffusion coefficient of 0.031 m2 s−1 and an edge convective velocity of −0.5 m s−1. Because of the large uncertainties in the source, it is not possible to pin down the exact value for the additional edge pinch. An upper limit for a possible edge convective velocity of −5 m s−1 was estimated. These findings could also be confirmed by analysing H-mode phases of a collisionality scan, in which the normalized collisionality varied from 3.5 to 5.5 at the pedestal top.

Dynamical coupling between magnetic equilibrium and transport in tokamak scenario modelling, with application to current ramps

The modelling of tokamak scenarios requires the simultaneous solution of both the time evolution of the plasma kinetic profiles and of the magnetic equilibrium. Their dynamical coupling involves additional complications, which are not present when the two physical problems are solved separately. Difficulties arise in maintaining consistency in the time evolution among quantities which appear in both the transport and the Grad–Shafranov equations, specifically the poloidal and toroidal magnetic fluxes as a function of each other and of the geometry. The required consistency can be obtained by means of iteration cycles, which are performed outside the equilibrium code and which can have different convergence properties depending on the chosen numerical scheme. When these external iterations are performed, the stability of the coupled system becomes a concern. In contrast, if these iterations are not performed, the coupled system is numerically stable, but can become physically inconsistent. By employing a novel scheme (Fable E et al 2012 Nucl. Fusion submitted), which ensures stability and physical consistency among the same quantities that appear in both the transport and magnetic equilibrium equations, a newly developed version of the ASTRA transport code (Pereverzev G V et al 1991 IPP Report 5/42), which is coupled to the SPIDER equilibrium code (Ivanov A A et al 2005 32nd EPS Conf. on Plasma Physics (Tarragona, 27 June–1 July) vol 29C (ECA) P-5.063), in both prescribed- and free-boundary modes is presented here for the first time. The ASTRA–SPIDER coupled system is then applied to the specific study of the modelling of controlled current ramp-up in ASDEX Upgrade discharges.

Self-consistent transport simulations of COMPASS operation with optimized NBI

The COMPASS tokamak, a mid-sized flexible device with ITER-like shape, which can operate in H-mode, is starting its re-established operation at the Institute of Plasma Physics in Prague. A new 600 kW, 40 keV neutral beam injection (NBI) system is foreseen as a major upgrade. Reported here are predictive simulations with the ASTRA transport code, in which the FAFNER Monte-Carlo NBI code is, for the first time, self-consistently integrated. These simulations are carried out for several typical COMPASS scenarios with different magnetic fields, plasma currents and shapes. We compare ohmic scenarios with NBI-heated scenarios and show that NBI is able to significantly improve the plasma performance, particularly to attain Ti ≅ Te, which is the primary goal of the NBI system. The NBI performance is discussed in detail. The chosen energy of 40 keV is shown to be in many aspects optimum. Simulations also predict substantial losses—orbit losses are pronounced for counter-current injection and charge-exchange losses caused by beam-halo neutrals are raised due to high NBI particle input.

10.1007/s11452-008-2001-9

Results from experimental studies on the injection of high-energy neutral hydrogen beams into the plasma of the Globus-M spherical tokamak are reviewed. In the Introduction, the importance of these studies for implementing the controlled fusion research program and constructing the ITER tokamak is proved. Some problems related to the use of neutral beam injection in small and low-aspect-ratio tokamaks is analyzed. Results are presented from numerical simulations of the experiment by using the ASTRA transport code. It is shown that the use of neutral beam injection in the Globus-M tokamak ensures efficient ion heating and increases the plasma stored energy. The greater part of the review is devoted to the survey of experiments on the injection of 22-to 30-keV hydrogen and deuterium beams with a power of 0.4–0.8 MW into the plasma of the Globus-M spherical tokamak in a wide range of plasma currents and densities. The experimental results are analyzed and compared with the results of numerical simulations. The achievement of top plasma parameters is highlighted.

Simulation of Hybrid Operation Modes in ITER

As one of the international thermonuclear experimental reactor (ITER) primary operation modes, the hybrid mode aims at establishing plasmas with significant fusion power and low loop voltage to drive an inductive current to test reactor-relevant components in extended pulse lengths at high neutron fluence. In this paper, predictive modeling of the hybrid mode is presented. The potential of hybrid modes is investigated with respect to fusion performance and the non-inductive current drive fraction in ITER. Simulations are performed with the ASTRA transport code by employing a physics-based heat transport model. Here, the particle transport is prescribed. The effect of electron cyclotron current drive (ECCD) to establish a low magnetic shear in the center of the plasma is also discussed. The simulations show that fusion gains and the non-inductive current drive fractions of up to 8.4 and 49 %, respectively, can be achieved in hybrid modes at ITER.

Study of plasma heating in discharges with neutral beam injection in the Globus-M spherical tokamak

Results from experimental studies on the injection of high-energy neutral hydrogen beams into the plasma of the Globus-M spherical tokamak are reviewed. In the Introduction, the importance of these studies for implementing the controlled fusion research program and constructing the ITER tokamak is proved. Some problems related to the use of neutral beam injection in small and low-aspect-ratio tokamaks is analyzed. Results are presented from numerical simulations of the experiment by using the ASTRA transport code. It is shown that the use of neutral beam injection in the Globus-M tokamak ensures efficient ion heating and increases the plasma stored energy. The greater part of the review is devoted to the survey of experiments on the injection of 22-to 30-keV hydrogen and deuterium beams with a power of 0.4–0.8 MW into the plasma of the Globus-M spherical tokamak in a wide range of plasma currents and densities. The experimental results are analyzed and compared with the results of numerical simulations. The achievement of top plasma parameters is highlighted.

Analysis of ECRH switch on/off events in ASDEX Upgrade

In this paper transient phenomena related to the electron heat transport when electron cyclotron resonance heating (ECRH) power is switched on or off are investigated by predictive and interpretative transport analysis. In the latter two numerical approaches—one based on the transport code ASTRA and the other by COBRA code—are compared. The transport simulations were done in the ASTRA code based on a critical ∇Te/Te model. The results for the evolution of the electron temperature in steady state and transient phases are compared with the experiment. The changes of the heat diffusivity with the ECRH power are compared with the results of the transport calculations from the interpretative analysis. The critical ∇Te/Te model reproduces well both the heat diffusivity and the electron temperature evolution in the region outside the ECRH deposition, and the results show good agreement with the experimental data there. The model cannot recover the electron temperature changes inside the ECRH deposition region with accuracy due to the simple assumption made in transport below the threshold.

Rapid electron internal transport barrier formation during magnetic shear reversal in fully non-inductive TCV discharges

The rapid formation of an electron internal transport barrier (eITB) is observed during a slow evolution (≃200 ms) from a centrally peaked to a hollow current density profile, while all external actuators remain constant. The time constant for the barrier formation appears to be shorter than the electron energy confinement time. The improved confinement associated with the barrier formation occurs first in a localized region off-axis. Then the effects propagate to inner and outer flux surfaces on a confinement time scale. The temporal and spatial localizations of the barrier formation suggest a threshold in the magnetic shear profile that triggers the onset of the eITB. The threshold-like behaviour can be attributed to the sudden appearance of a minimum q (or zero-shear) flux surface in the safety factor profile. Based on modelling of the current profile evolution using the ASTRA transport code, the appearance of the zero-shear flux surface is correlated with the temporal and spatial formation of the barrier.

Sawtooth control experiments on ASDEX Upgrade

In a fusion device, the so-called sawtooth instability can lead to the triggering of confinement limiting neoclassical tearing modes. On the other hand, the existence of sawteeth is desirable for the removal of one fusion product, i.e. helium ash from the plasma core. This has led to great interest in the control of sawteeth. The sawtooth period can be changed drastically by local modification of the q-profile. In this paper, the influence of the beam line geometry of the neutral beam injection in the ASDEX Upgrade tokamak will be presented as well as the effect of local electron cyclotron current drive. Systematic scans in the electron cyclotron current deposition from the high-field side to the low-field side resolve areas with sawtooth stabilization and destabilization. These observations will be discussed, including modelling of the main results, with the ASTRA transport code constrained by experimental data.

Importance of electron cyclotron wave energy transport in ITER

The importance of electron cyclotron (EC) wave emission to the local electron power balance is analysed for various ITER operation regimes and, for comparison, for typical working conditions of FIRE, IGNITOR and the reactor-grade ITER concept as considered during the Engineering Design Phase (ITER-EDA). To cover the non-local effects in EC wave emission as well, the CYTRAN routine along with the ASTRA transport code is used. As a result, EC wave emission is shown to be a significant contributor to core electron cooling if the core electron temperature is about 35 keV or higher, as expected for ITER and tokamak reactor steady-state operation; in fact, it becomes the dominant core electron cooling mechanism at temperatures exceeding 40 keV, as such affecting the core plasma power balance in an important way.

Simulation of high-Z impurity behaviour for ITER operational scenarios using the ZIMPUR impurity code

Results of the simulation of the transport and radiation losses of high-Z impurities (tungsten and argon) in the ITER reference operational scenarios are presented. The impurity dynamics was modelled by the ZIMPUR impurity code, a description of which is presented. This code was integrated with the ASTRA transport code for the background plasma behaviour modelling and with the NCLASS code to take into account the neoclassical impurity fluxes. Simulations show that for flat plasma density profiles the neoclassical thermal diffusion contributes to plasma core screening from heavy impurities in all considered scenarios. Thus, a radiating layer is formed near the plasma column periphery. It is more essential for the steady-state scenario with the reversed shear region and an improved confinement in the plasma core. An appreciable effect is also found for the reference inductive ELMy H-mode scenario, where the plasma is more strongly influenced by anomalous transport. The calculated radiated power near the plasma edge exceeds by about twice the value obtained in the coronal model approximation. This can be explained as being due to the reduction of impurity ion charge states, due to their charge exchange with deuterium/tritium neutrals, fuelling the plasma. It offers the possibility of decreasing the total impurity contamination, which is necessary for re-radiation of the given power.

ELM triggering conditions for the integrated modeling of H-mode plasmas

Recent advances in the integrated modeling of ELMy H-mode plasmas are presented. A model for the H-mode pedestal and for the triggering of ELMs predicts the height, width, and shape of the H-mode pedestal and the frequency and width of ELMs. Formation of the pedestal and the L-H transition is the direct result of ExB flow shear suppression of anomalous transport. The periodic ELM crashes are triggered by either the ballooning or peeling MHD instabilities. The BALOO, DCON, and ELITE ideal MHD stability codes are used to derive a new parametric expression for the peeling-ballooning threshold. The new dependence for the peeling-ballooning threshold is implemented in the ASTRA transport code. Results of integrated modeling of DIII-D like discharges are presented and compared with experimental observations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.

Studies on Pellet Fueling of ITER-Like Plasmas

The paper reports on simulation of pellet-fueled plasmas in a fusion reactor. The simulations have been performed by means of the ASTRA transport code. We have studied physical modeling of pellet injection as well as the numerical conditions to resolve pellet injection correctly. As a first step the essential mechanisms for density control have been studied based on simplified assumptions with a generic source of additional heating. The experience gained has been used to simulate advanced scenarios including internal transport barriers. It has been confirmed that it is possible to drive the plasma of a next-generation tokamak into a high-Q regime and to maintain it in a steady-state regime. Nevertheless, the pellet injection parameters required are rather demanding and imply a significant technological improvement of pellet injectors. Those investigations represent an improvement of simulations done earlier with a control of the central density at constant profile.